Definition:Non-Pythagorean Prime

Definition

A non-Pythagorean prime is an odd prime number of the form:

$p = 4 n + 3$

where $n \in \Z_{\ge 0}$ is a positive integer.

Sequence

The sequence of non-Pythagorean primes begins:

$\begin{array} {r | r } p & 4 n + 3 \\ \hline 3 & 4 \times 0 + 3 \\ 7 & 4 \times 1 + 3 \\ 11 & 4 \times 2 + 3 \\ 19 & 4 \times 4 + 3 \\ 23 & 4 \times 5 + 3 \\ 31 & 4 \times 7 + 3 \\ 43 & 4 \times 10 + 3 \\ 47 & 4 \times 17 + 3 \\ \end{array}$

Also see

• Fermat's Two Squares Theorem: such a prime number is never the sum of two squares

• Definition:Pythagorean Prime